Several industrial or scientific applications require fabrication of sharp, pointed tips composed of different materials that cannot be readily formed or etched into the required shapes at a desired level of precision. These applications include: scanning probe microscopy, field emission using emitter arrays of sharp tips, and material abrasion using arrays of sharp geometrical protrusions, etc. Known methods of forming such tips include the deposition of the desired tip material into crystallographic molds formed by patterning and subsequent etching of single crystal substrates e.g. U.S. Pat. No. 5,221,415 (Albrecht), hereby incorporated by reference in its entirety. Typical substrates for such molds in the art include single crystal <100> silicon surfaces in which “V-shaped” grooves or other shaped indentations are formed. This is followed by deposition of the desired tip material into the groove and then release of the tip structure by dissolving or removal of the Si mold or substrate. The most commonly used crystallographic etchants used to form V-grooves in silicon substrates are alkaline solutions (e.g. KOH, TMAH, etc.). These etchants and processes exploit the relative perfection of facet formation that occurs in such crystal-orientation-dependent etching processes. Such a V-groove is defined by four (111) slow etching facets forming a 4-sided pyramid with a square base as shown in the Albrecht patent. Nearly geometrically perfect 4-sided pyramidal V-grooves can be obtained if the etch is started from a perfect square or perfect circle window in the masking material, e.g. photoresist, SiO2, SiN, or other masking material, often used in combination with photoresist being used to pattern a hard-mask material such as SiO2, SiNx. However, geometrical perfection of the openings in a masking material is limited by the precision of the patterning process. Even for the most precise and most expensive available patterning equipment (steppers or e-beam lithography) and etches used for example in the printing of contact windows in current generations of integrated circuits, the minimum X-Y mismatch for a square window is limited to about 5-20 nm. For the case of scanning probe tips, for which a desirable tip radius is in the range of below 10 nm, this level of X-Y mismatch becomes the limiting factor which determines the relative sharpness of the tip. Because of these X-Y imperfections in the mask itself, lithography process limitations (e.g. roughness of photoresist side walls), masking layer etch imperfections (e.g. residues left on the surface or slightly asymmetrical over-etching), imperfect subsequent etching of the V-groove (i.e. crystal defects, hydrogen bubbles, stirring direction, position of wafer in solution during etching), four-faceted pyramidal grooves always end in wedges, rather than a single 4-sided point. If the wedge shape (and resultant tip radius) is larger than about 20 nm, even an additional step of oxidation sharpening, e.g., as disclosed in U.S. Pat. No. 5,580,827 (Akamine), hereby incorporated by reference in its entirety, is insufficient to form a single four-pointed pyramidal mold and resultant tip after processing. FIG. 1-5 shows how such wedge-terminated oxidation-sharpened pyramidal V-grooves can lead to double-tipped probes, both points of which are quite sharp.